Answer:
34.8°
Explanation:
Given the following :
Number of lines (N) = 587mm
529mm to m = 587*1000 = 587000 per meter
d = 1 / N ; 1/587000 = 0.00000170357
Wavelength of light waves :
λ1 = 497nm = 497 × 10^-9 m
λ2 = 251nm = 251 × 10^-9 m
Angular position in 3rd order; m=3
For
λ1 ; dsinθ3 = 3λ1 ;
λ2 = dsinθ3 = 3λ2
Substituting values
dsinθ3 = 3λ1 =
0.00000189 * sinθ3 = 3 * 497 × 10^-9
θ3(1) = sin^-1(1491 * 10^-9 / 0.00000170357)
θ3(1) = sin^-1(0.8752208)
θ3(1) = 61.07°
λ2 = dsinθ3 = 3λ2
0.00000189 * sinθ3 = 3 * 251 × 10^-9
θ3(2) = sin^-1(753 * 10^-9 / 0.00000170357)
θ3(1) = sin^-1(0.4420129)
θ3(1) = 26.23°
Angular separation :
61.07° - 26.23° = 34.84°
34.8°
